Nonparametric goodness‐of‐fit testing for parametric covariate models in pharmacometric analyses

The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. Although covariate selection criteria have been studied extensively, the choice of the functional relationship between covariates and parameters, however, has received much less attention. Often, a simple particular class of covariate‐to‐parameter relationships (linear, exponential, etc.) is chosen ad hoc or based on domain knowledge, and a statistical evaluation is limited to the comparison of a small number of such classes. Goodness‐of‐fit testing against a nonparametric alternative provides a more rigorous approach to covariate model evaluation, but no such test has been proposed so far. In this manuscript, we derive and evaluate nonparametric goodness‐of‐fit tests for parametric covariate models, the null hypothesis, against a kernelized Tikhonov regularized alternative, transferring concepts from statistical learning to the pharmacological setting. The approach is evaluated in a simulation study on the estimation of the age‐dependent maturation effect on the clearance of a monoclonal antibody. Scenarios of varying data sparsity and residual error are considered. The goodness‐of‐fit test correctly identified misspecified parametric models with high power for relevant scenarios. The case study provides proof‐of‐concept of the feasibility of the proposed approach, which is envisioned to be beneficial for applications that lack well‐founded covariate models.